Download Geometry Diff Chapter 4 Review Answers page 315 #1 – 16, 18, 19

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Geometry Diff
Chapter 4
Review Answers
page 315 #1 – 16, 18, 19
1.
Equiangular and Equilateral
2.
Right and Scalene
3.
Obtuse and Isosceles
4.
m∠1 = 180 −125 = 55°
5.
m∠2 = 180 − m∠4 − 32 = 180 −125 − 32 = 23°
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6.
m∠3 = 125 − 62 = 63°
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7.
m∠4 = 125° because of vertical angles
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8.
x + 21 = 2x −14 ⇒ x = 35
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9.
4 y −10 = 3y + 5 ⇒ y = 15
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10.
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As a flow proof
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As a 2-column proof
a)
b)
c)
d)
e)
f)
XY || WZ
∠2 ≅ ∠4
XW || YZ
∠2 ≅ ∠4
XZ || XZ
ΔXWZ ≅ ΔZYX
a)
b)
c)
d)
e)
f)
Given
Alt. Int. ∠ Thrm
Given
Alt Int. ∠ Thrm.
Reflex. POC
ASA
11.
x = 180 − 76 − 76 = 28° , which is answer C
12.
TJ =
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SE =
(0 − (−4))2 + (5 − (−2))2 = 4 2 + 72 = 16 + 49 = 65
(3 − (−1))2 + (10 − 3)2 = 4 2 + 72 = 16 + 49 = 65
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JD =
(1 − 0) 2 + ( −1 − 5) 2 = 12 + (−6) 2 = 1+ 36 = 37
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EK =
( 4 − 3) 2 + ( 4 −10) 2 = 12 + ( −6) 2 = 1+ 36 = 37
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TD =
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SK =
(1 − (−4))2 + (−1 − (−2))2 = 52 +12 = 25 +1 =
(4 − (−1))2 + (4 − 3)2 = 52 +12 = 25 +1 = 26
Since each pair of corresponding sides are congruent, then the triangles are congruent by SSS.
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26
13.
AAS (have reflexive side)
14.
SSS (have reflexive side)
15.
Not Possible (only have reflexive side)
16.
SAS (have reflexive side)
18.
m∠1 = 66° , because the base angles of an isosceles triangle are congruent
19.
m∠2 = 180 − 24 − m∠4 with m∠4 = 66 + 66 = 132° (Exterior angle equals the sum of the remote
interior angles), therefore m∠2 = 180 − 24 −132 = 24°
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